Quantification of thermal ring flexibilities of aromatic and heteroaromatic compounds

Abstract

The consequences of thermal fluctuations occurring at room temperatures on the aromatic character of a broad group of compounds were analyzed in three distinct ways. First of all, the ring deformations were modeled along normal coordinates coming from quantum thermo-chemistry computations. The amplitudes of vibrations were estimated according to absorbed energies at room temperature. Alternatively, in-plane and out-of-plane ring deformations were modeled via scanning procedure with partial relaxation of the molecular geometry. The influence of ring deformations on π-electron delocalization was expressed in terms of HOMA values. Besides, the ring deformability was defined as the averaged change of bond angles or dihedral angles constituting the ring that was associated with 1.5 kcal mol(-1) increase of the system energy. The molecules structures adopted during vibrations at room temperature can lead to significant heterogeneity of structural index of aromaticity. The broad span of HOMA values was obtained for analyzed five- or six-membered aromatic and heteroaromatic rings. However, the averaged values obtained for such fluctuations almost perfectly match HOMA values of molecule in the ground state. It has been demonstrated that the ring deformability imposed by bond angle changes is much smaller than for dihedral angles with the same rise of system energy. Interestingly in the case of out-of-plane vibrations modeled by scanning procedure there is observed linear correlation between ring deformability and HOMA values. Proposed method for inclusion of thermal vibrations in the framework of π-electron delocalization provides natural shift of the way of thinking about aromaticity from a static quantity to a dynamic and heterogeneous one due to inclusion of a more realistic object of analysis - thermally deformed structures. From this perspective the thermal fluctuations are supposed to be non-negligible contributions to aromaticity phenomenon.

Fig. 1

Schematic representation of structures of analyzed aromatic and heteroaromatic compounds

Fig. 2

The heterogeneity of aromatic character induced by thermal vibrations (black circles), in-plane deformations (gray circles) and out-of-plane distortions (open circles). All geometry alterations correspond to increase of system energy not extending 1.5 kcal/mol

Fig. 3

The ring deformability (RD are expressed in degrees) corresponding to averaged values of bond angles or torsion angles changes that were correlated with 1.5 kcal mol^-1 increase of energy from the ground state of aromatic or heteroaromatic compounds. In-plane vibrations are defined as bond angle changes, while torsion changes are responsible for out-of-plane fluctuation

Fig. 4

The ring deformability (expressed in degrees) corresponding to averaged changes of bond angles or torsion angles associated with not higher than 1.5 kcal/mol energy increase with respect of the ground state

Fig. 5

The correlation HOMA values and out-of-plane phenyl ring deformations in a variety of cyclophane systems

Fig. 6

The correlation between in-plane and out-of-plane deformations for optimized structures of different cyclophanes analogues (see Fig. 5 for chemical structures)

Fig. 7

Correlation between HOMA values characterizing ground state and mean value of thermally excited geometries at room temperature. Values of SDV (standard deviation of population variance) were also provided